Trianon Palace hotel which is located in the wooded area behind the Chateau and has a great outdoor eating area. The Gordon Ramsey restaurant is in the hotel but there's a separate restaurant (possibly managed by the same staff?) that's more reasonable.

We were just at Versailles on Sunday. My strong advice is grab some charcuterie, a few apples and some great cheese at a market or appropriate stores in Paris, pick up a baguette that morning, and have a pinic to remember on the grounds. Oops, don't forget a bottle of Burgundy, or your other favourite wine.

Note that when you visit the Chateau/palace (which is well worth doing) they will make you check a bag that contains, food, wine, corkscrews and knifves, but you can get it back as soon as you leave the building, before you explore the grounds.

For those driving: Parking is available under the Square (hope your magnetic exit card works better than ours did, but the attendants were helpful in light of my poor French). It seems to fit your description, and we would happily return. -- Jake